In real estate listings what is the definition of off market?

Well this really depends. Generally, off the market is a subcategory. For example, the listing can say:

POM: This means permanently off the market

TOM: This can mean Temporarily off the market

If the listing doesn't designate the status more specifically, I would suggest calling the broker associated with the listing and see if it is simply off the market because the owner decided not to sell or rent.

Think Properties NYC